This application claims the benefit of Japanese Application No. 2002-045494 filed Feb. 22, 2002.
The present invention relates to a backprojection method and an X-ray CT (computed tomography) apparatus, and more particularly to a backprojection method and an X-ray CT apparatus by which backprojection processing can be simplified and sped up.
The current mainstream X-ray CT apparatus implements a filtered backprojection technique involving processes of data collection, preprocessing, filtering, backprojection processing, and post-processing to thereby reconstruct an image.
Conventional backprojection processing is disclosed in, for example, Japanese Patent Application Laid Open No. H8-187241 and U.S. Pat. No. 5,414,622.
In such backprojection processing, projection data D0(view, ch) obtained by a fan beam represented by a view angle view and a detector channel ch is subjected to a calculation for projecting the projection data D0(view, ch) onto coordinates (x, y) of a pixel constituting a reconstruction region to obtain backprojection pixel data D2(x, y), and the backprojection pixel data D2(x, y) for all views employed in image reconstruction are added to obtain backprojection data D3(x, y).
In the conventional backprojection processing, a calculation for obtaining the backprojection pixel data D2(x, y) from the projection data D0(view, ch) must be conducted for, for example, 512xc3x97512 pixels, in which the projection data D0(view, ch) line up along arc-shaped geometrical positions corresponding to an arc-like shape of the detector, and the backprojection pixel data D2(x, y) line up along geometrical positions on rectangular coordinates of a reconstruction region. This raises the problems that the processing is intricate and time-consuming.
It is therefore an object of the present invention is to provide a backprojection method and an X-ray CT apparatus by which backprojection processing can be simplified and sped up.
The present invention, in accordance with its first aspect, provides a backprojection method characterized in comprising the steps of: obtaining axially projected data D1 by projecting projection data D0(view, ch) obtained by a fan beam represented by a view angle view and a detector channel ch onto a straight projection axis; then, obtaining backprojection pixel data D2 by projecting said axially projected data D1 onto pixels constituting a reconstruction region; and obtaining backprojection data D3 by adding the backprojection pixel data D2 for all views employed in image reconstruction on a pixel-to-pixel basis.
In the backprojection method of the first aspect, instead of obtaining the backprojection pixel data D2 directly from the projection data D0(view, ch), axially projected data D1(view, pt) is obtained from the projection data D0(view, ch), and then backprojection pixel data D2(x, y) is obtained from the axially projected data D1. The symbol pt represents a coordinate on the projection axis.
Although the calculation for obtaining the axially projected data D1(view, pt) lining up along geometrical positions on a straight projection axis from the projection data D0(view, ch) lining up along arc-shaped geometrical positions corresponding to an arc-like shape of the detector has a processing load per datum identical to that of a conventional calculation for obtaining backprojection pixel data D2(x, y) from the projection data D0(view, ch), the number of data is no more than about 8,000, for example, which is only {fraction (1/30)} of that of the conventional 512xc3x97512 pixels. On the other hand, although the calculation for obtaining the backprojection pixel data D2 from the axially projected data D1 requires calculations for 512xc3x97512 pixels as in the prior art, the calculation for obtaining the backprojection pixel data D2(x, y) lining up on rectangular coordinates from the axially projected data D1(view, pt) lining up along a straight line needs only simple processing involving mere sampling at a regular pitch and multiplication by a distance factor. Thus, as a whole, the backprojection processing can be simplified and sped up.
The present invention, in accordance with its second aspect, provides the backprojection method of the aforementioned configuration, characterized in that when a direction of a center axis of the fan beam at views=0xc2x0 is represented by a y-direction and a direction orthogonal to the y-direction and parallel to a fan beam plane is represented by an x-direction, said projection axis is defined as a straight line passing through a center of reconstruction and parallel to the x-direction for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 135xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity; and said projection axis is defined as a straight line passing through the center of reconstruction and parallel to the y-direction for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity.
Note that view=xe2x88x9245xc2x0 and view=315xc2x0 are separately expressed herein for convenience of representation, but they are the same and represent the same view in reality.
When data is projected onto a straight projection axis, accuracy increases as the angle formed between the projection direction line and the projection axis approaches 90xc2x0, and accuracy decreases as the angle approaches 0xc2x0.
In the backprojection method of the second aspect, since the angle formed between the projection direction line and the projection axis never falls below about 45xc2x0, reduction in accuracy is prevented.
The present invention, in accordance with its third aspect, provides the backprojection method of the aforementioned configuration, characterized in that one axially projected datum D1 is obtained by interpolation calculation from a plurality of projection data D0.
The number of projection data D0 and the positional intervals thereof at one view angle are determined by the detector. Specifically, the number of projection data D0 is xe2x80x9cthe number of channels of the detector (e.g., 1,000)xe2x80x9d, and the positional intervals of the projection data D0 are xe2x80x9cthe channel pitch of the detector (e.g., 1 mm)xe2x80x9d.
In the backprojection method of the third aspect, since one axially projected datum D1 is obtained by interpolation calculation from a plurality of projection data D0, the number of the axially projected data D1(e.g., 3,500 per view angle) and the data intervals thereof (e.g., 1 mm) on the projection axis can be selected without limitation by the number and position intervals of the projection data D0.
The present invention, in accordance with its fourth aspect, provides the backprojection method of the aforementioned configuration, characterized in that addresses of the plurality of projection data D0 and interpolation factors for obtaining the one axially projected datum D1 are set in a table.
Although the addresses of the plurality of projection data D0 and interpolation factors for obtaining the one axially projected datum D1 may be calculated each time the one axially projected datum D1 is to be obtained, the time of the calculation is an overhead.
In the backprojection method of the fourth aspect, this overhead is eliminated by calculating beforehand the addresses of the plurality of projection data D0 and interpolation factors and setting them in a table.
The present invention, in accordance with its fifth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: obtaining one axially projected datum D1 by interpolation calculation from a plurality of projection data D0; setting in a table addresses of the plurality of projection data D0 and interpolation factors for obtaining the one axially projected datum D1 for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and using said table for other view angle ranges.
Considering a case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by 180xc2x0 around the center of reconstruction for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity. Therefore, the addresses of the projection data D0 and the interpolation factors for obtaining one axially projected datum D1 can be used in common in these view angle ranges.
Moreover, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by xe2x88x9290xc2x0 around the center of reconstruction for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the addresses of the projection data D0 and the interpolation factors for obtaining one axially projected datum D1 can be used in common in these view angle ranges.
Furthermore, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the X-ray tube, detector and projection axis is rotated by 90xc2x0 around the center of reconstruction for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the X-ray tube, detector and projection axis for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the addresses of the projection data D0 and the interpolation factors for obtaining one axially projected datum D1 can be used in common in these view angle ranges.
In the backprojection method of the fifth aspect, since a table used for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view  less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity is used in common for other view angle ranges, the storage capacity required for the table is reduced.
The present invention, in accordance with its sixth aspect, provides the backprojection method of the aforementioned configuration, characterized in that the backprojection pixel data D2 are obtained by transformation calculation from the axially projected data D1.
The number of the axially projected data D1 is, for example, 8,000, and the number of the backprojection pixel data D2 is, for example, 512xc3x97512. Therefore, the effect of speedup is larger in simplifying the calculation for obtaining the backprojection pixel data D2 from the axially projected data D1 than in simplifying the calculation for obtaining the axially projected data D1 from the projection data D0.
In the backprojection method of the sixth aspect, since the backprojection pixel data D2 is obtained from the one axially projected datum D1, transformation calculation simpler than the interpolation calculation, involving only sampling at a regular pitch and multiplication by a distance factor is merely required, thus enhancing the effect of speedup.
The present invention, in accordance with its seventh aspect, provides the backprojection method of the aforementioned configuration, characterized in that parameters for said transformation calculation are set in a table.
Although the parameters for the transformation calculation may be calculated each time the one backprojection pixel datum D2 is to be obtained, the time of the calculation is an overhead.
In the backprojection method of the seventh aspect, this overhead is eliminated by calculating beforehand the parameters for the transformation calculation and setting them in a table.
The present invention, in accordance with its eighth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: obtaining one backprojection pixel datum D2 by transformation calculation from one axially projected datum D1; setting in a table parameters for the transformation calculation for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and using said table for other view angle ranges.
Considering a case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by 180xc2x0 around the center of reconstruction for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D2 from the axially projected data D1 can be used in common in these view angle ranges.
Moreover, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by xe2x88x9290xc2x0 around the center of reconstruction for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D2 from the axially projected data D1 can be used in common in these view angle ranges.
Furthermore, considering a case in which the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, when the geometrical relationship of the projection axis and reconstruction region is rotated by 90xc2x0 around the center of reconstruction for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity, the geometrical relationship coincides with that of the projection axis and reconstruction region for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity in the case in which the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction. Therefore, the parameters for the transformation calculation for obtaining the backprojection pixel data D2 from the axially projected data D1 can be used in common in these view angle ranges.
In the backprojection method of the eighth aspect, since a table used for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity is used in common for other view angle ranges, the storage capacity required for the table is reduced (for example, to xc2xc in a 360xc2x0 full scan).
The present invention, in accordance with its ninth aspect, provides the backprojection method of the aforementioned configuration, characterized in further comprising the steps of: separately conducting addition of the backprojection pixel data D2 for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, and addition of the backprojection pixel data D2 for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and obtaining the backprojection data D3 by finally adding the sums from the additions.
When the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, the processing is easier by a method involving the step of obtaining the backprojection pixel data D2 with the fixed y-coordinate and varying x-coordinate, and repeating the step with the varying y-coordinate. On the other hand, when the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, the processing is easier by a method involving the step of obtaining the backprojection pixel data D2 with the fixed x-coordinate and varying y-coordinate, and repeating the step with the varying x-coordinate. However, this requires separate algorithms for these methods.
In the backprojection method of the ninth aspect, since addition of the backprojection pixel data D2 for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, i.e., addition when the projection axis is defined as a straight line parallel to the x-axis direction of the reconstruction plane and passing through the center of reconstruction, is conducted separately from addition of the backprojection pixel data D2 for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity, i.e., addition when the projection axis is defined as a straight line parallel to the y-axis direction of the reconstruction plane and passing through the center of reconstruction, confusion of data is avoided when x and y are switched, and the algorithm can be used in common. It should be noted that when the backprojection data D3(x, y) is obtained by finally adding the sums from these additions, it is necessary to transform coordinates so that x and y match in the two sums.
The present invention, in accordance with its tenth aspect, provides an X-ray CT apparatus characterized in comprising: an X-ray tube; a detector for detecting X-rays of a fan beam; scanning means for collecting projection data D0(view, ch) represented by a view angle view and a detector channel ch while rotating at least one of said X-ray tube and said detector around a subject to be imaged; axially projected data calculating means for obtaining axially projected data D1 by projecting said projection data D0(view, ch) onto a straight projection axis; backprojection pixel data calculating means for obtaining backprojection pixel data D2 by projecting said axially projected data D1 onto pixels constituting a reconstruction region; and backprojection data calculating means for obtaining backprojection data D3 by adding the backprojection pixel data D2 for all views employed in image reconstruction on a pixel-to-pixel basis.
In the X-ray CT apparatus of the tenth aspect, the backprojection method of the first aspect can be suitably implemented.
The present invention, in accordance with its eleventh aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that when a direction of a center axis of the fan beam at view=0xc2x0 is represented by a y-direction and a direction orthogonal to the y-direction and parallel to a fan beam plane is represented by an x-direction, said axially projected data calculating means defines said projection axis as a straight line passing through a center of reconstruction and parallel to the x-direction for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity; and defines said projection axis as a straight line passing through the center of reconstruction and parallel to the y-direction for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity.
In the X-ray CT apparatus of the eleventh aspect, the backprojection method of the second aspect can be suitably implemented.
The present invention, in accordance with its twelfth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means obtains one axially projected datum D1 by interpolation calculation from a plurality of projection data D0.
In the X-ray CT apparatus of the twelfth aspect, the backprojection method of the third aspect can be suitably implemented.
The present invention, in accordance with its thirteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means uses a table in which addresses of the plurality of projection data D0 and interpolation factors for obtaining the one axially projected datum D1 are set.
In the X-ray CT apparatus of the thirteenth aspect, the backprojection method of the fourth aspect can be suitably implemented.
The present invention, in accordance with its fourteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said axially projected data calculating means obtains one axially projected datum D1 by interpolation calculation from a plurality of projection data D0; sets in a table addresses of the plurality of projection data D0 and interpolation factors for obtaining the one axially projected datum D1 for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity, and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and uses said table for other view angle ranges.
In the X-rav CT apparatus of the fourteenth aspect, the backprojection method of the fifth aspect can be suitably implemented.
The present invention, in accordance with its fifteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means obtains the backprojection pixel data D2 by transformation calculation from the axially projected data D1.
In the X-ray CT apparatus of the fifteenth aspect, the backprojection method of the sixth aspect can be suitably implemented.
The present invention, in accordance with its sixteenth aspect, provides the X-ray Cr apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means uses a table in which parameters for said transformation calculation are set.
In the X-ray Cf apparatus of the sixteenth aspect, the backprojection method of the seventh aspect can be suitably implemented.
The present invention, in accordance with its seventeenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said pixel projection data calculating means obtains one backprojection pixel datum D2 by transformation calculation from one axially projected datum D1; sets in a table parameters for the transformation calculation for any one of a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity,l and a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and uses said table for other view angle ranges.
In the X-ray CT apparatus of the seventeenth aspect, the backprojection method of the eighth aspect can be suitably implemented.
The present invention, in accordance with its eighteenth aspect, provides the X-ray CT apparatus of the aforementioned configuration, characterized in that said backprojection data calculating means separately conducts addition of the backprojection pixel data D2 for a view angle range of xe2x88x9245xc2x0xe2x89xa6view less than 45xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 135xc2x0xe2x89xa6view less than 225xc2x0 or a view angle range mainly including the range and also including its vicinity, and addition of the backprojection pixel data D2 for a view angle range of 45xc2x0xe2x89xa6view less than 135xc2x0 or a view angle range mainly including the range and also including its vicinity and for a view angle range of 225xc2x0xe2x89xa6view less than 315xc2x0 or a view angle range mainly including the range and also including its vicinity; and obtains the backprojection data D3 by finally adding the sums from the additions.
In the X-ray CT apparatus of the eighteenth aspect, the backprojection method of the ninth aspect can be suitably implemented.
According to the backprojection method and X-ray CT apparatus of the present invention, since axially projected data D1(view, pt) are first obtained from projection data D0(view, ch), and then backprojection pixel data D2(x, y) are obtained from the axially projected data D1(view, pt), instead of obtaining the backprojection pixel data D2(x, y) directly from the projection data D0(view, ch), the backprojection processing can be simplified and sped up.
Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.